Just 12 hours after winning their respective primaries in the race for US Senate, Republican Gabriel E. Gomez and his Democratic rival, Representative Edward J. Markey, wasted no time launching sharp general election attacks.

Greeting commuters at the Broadway MBTA station in South Boston early Wednesday, Gomez called Markey the “poster boy for term limits” and challenged him to three debates. He then flatly refused to sign the so-called People’s Pledge, an agreement to keep outside interests from influencing the campaign.

“I think it’s the height of hypocrisy when Congressman Markey, who’s been taking outside money for the last 30 years from groups he regulates and has control over, and now he wants to ask me to do the same thing? I’m pretty clear on where I stand,’’ Gomez said.

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Taking the podium at the Omni Parker House hotel several hours later, Markey went on the attack against Gomez, painting him as someone who would thwart the agenda of President Obama.

I am “going to go out and deliver our message to independent voters all across our state that President Obama has the vision for what our country needs to do in order to have a brighter future,” Markey said.

Obama comfortably won Massachusetts in his 2012 re-election effort.

Markey again challenged Gomez to sign the pledge that curbs spending from third-party groups. Markey and his Democratic rival, Representative Stephen F. Lynch had signed such a pledge in the primary.

“I am going to challenge him today and I am going to challenge him every day to take the People’s Pledge,” Markey said.

Addressing Gomez’s debate challenge, Markey said the discussions about debates had not yet begun. But he said the two nominees “will be debating. You don’t have to worry about that.” The debates, he said, would highlight large differences between the two candidates on the issues.

“I’m looking forward to having those differences be put out there in stark contrast for the people of Massachusetts to understand,” he said.

Markey appeared at the Parker House standing arm and arm with Lynch, who pledged to support the Democratic nominee in his bid for US Senate, now that the contentious primary is behind them.

“I am eager to be a full-throated, if I could, supporter of Ed Markey as our next US senator,” said Lynch, who is recovering from an illness that had left his voice hoarse.

The general election to fill the seat vacated by John F. Kerry is scheduled for June 25.